First you have to extract the values from the map. Then you can use a sort method implementation from native java, with your custom comparator.
Map<String, Object[]> data = new HashMap<String, Object[]>();
List<Object[]> values = new ArrayList<Object[]>();
values.addAll(data.values());
Collections.sort(values, new Comparator<Object[]>()
{
    @Override
    public int compare(Object[] o1, Object[] o2)
    {
        // TODO implement me
        // o1 less than o2 ? return -1
        // o1 greater than o2 ? return 1
        // o1 equals o2 ? return 0
    }
});
In this example you only need to implement the compare method. From the docs:
Compares its two arguments for order. Returns a negative integer,
  zero, or a positive integer as the first argument is less than, equal
  to, or greater than the second.
You can also take a look at: Sort ArrayList of custom Objects by property